Current state-of-the-art transceivers in fiber optical communication systems can produce data streams with a bit rate up to 200 Gb/s. Such high bit rate signals can for example be generated using a classic serial on-off keying transmission, but this has two main disadvantages. First, such an approach requires large-bandwidth electronics. Second, the spectral efficiency of the resulting optical signal is very low, which generally leads to an unacceptable spectral occupancy.
In view of these disadvantages, advanced modulation formats such as quadrature phase shift keying (QPSK) and 16 quadrature amplitude modulation (16 QAM) have been adopted for higher bit rates. Here, the symbol rate is lower than the bit rate, leading to a higher spectral efficiency than provided by serial on-off keying transmission, and the spectral efficiency can be additionally doubled by performing polarization-division multiplexing (PDM).
Such advanced modulation formats combined with PDM require coherent detection, as all dimensions of the optical field must be analyzed for proper signal demodulation. Besides enabling the demodulation of advanced modulation formats, coherent detection has two additional benefits: increased receiver sensitivity and possibility of digital impairment compensation. Digital compensation of transmission impairments such as chromatic dispersion (CD) and polarization-mode dispersion (PMD) has been extensively investigated and has been applied in commercially available transponders. An effective compensation of the respective impairments requires precise impairment estimation, commonly referred to as channel estimation.
Different algorithms for channel estimation in coherent optical transceivers have been proposed and implemented using for example digital signal processing (DSP) architectures. For example, FIG. 1 illustrates a corresponding digital signal processing (DSP) architecture of a channel estimator 10. In this architecture, a digitalized optical signal 20 is processed by a bulk chromatic dispersion (CD) equalizer 30. Commonly, this type of equalizer is implemented in the frequency domain and is then referred to as Frequency Domain Equalizer (FDE) 30. The Frequency Domain Equalizer (FDE) 30 coarsely compensates the chromatic dispersion (CD), leaving the resulting signal 40 with a residual chromatic dispersion (CD). The resulting signal 40 should have sufficiently low residual chromatic dispersion (CD) in order to enable the subsequent steps of frame detection 60, frequency offset correction 70, and finally MIMO equalization 80 to be performed in a robust manner.
As illustrated in FIG. 1, a chromatic dispersion estimator 50 receives information from the Frequency Domain Equalizer (FDE) 30, and based on this information, the chromatic dispersion estimator 50 configures the Frequency Domain Equalizer (FDE) 30. In other words, the amount of residual chromatic dispersion CD left by the Frequency Domain Equalizer (FDE) 30 largely depends on the performance of the chromatic dispersion estimator 50. Moreover, since the performance of the subsequent stages of frame detection 60, frequency offset correction 70, and finally MIMO equalization 80 located after the Frequency Domain Equalizer (FDE) 30 depends on the Frequency Domain Equalizer (FDE) 30, the chromatic dispersion estimator 50 is conventionally located immediately before or after the Frequency Domain Equalizer (FDE) 30 for improved performance
A conventional chromatic dispersion estimator 50 is based on the constant-modulus algorithm (CMA), as for example described in Kuschnerov, Maxim, et al. “Adaptive chromatic dispersion equalization for non-dispersion managed coherent systems.” Optical Fiber Communication Conference. Optical Society of America, 2009. The constant-modulus algorithm (CMA) assumes that all constellation symbols of the received signal 20 have identical amplitudes, such as for example QPSK modulation symbols, since all symbols of the QPSK constellation have identical amplitudes. In other words, the constant-modulus algorithm (CMA) considers the amplitude (modulus) of such a signal to be constant as long as it is not subject to any impairment. However, if chromatic dispersion distorts the signal, the original constellation shape no longer holds, meaning that the signal no longer has constant amplitude over time. In this case, the constant-modulus algorithm based chromatic dispersion (CMA-based CD) estimator 50 applies different chromatic dispersion test values to the Frequency Domain Equalizer (FDE) 30, and analyses the Frequency Domain Equalizer (FDE) output signal 40. For a given chromatic dispersion test value, the amplitude of the output signal is constant. In ideal conditions, this corresponds exactly to the opposite value of the chromatic dispersion imposed by the link and thus provides an optical equalization of the signal.
However, the accuracy of the CMA-based CD estimator is affected by different factors. First, as discussed above, the CMA-based algorithm is not agnostic to the modulation format, as it assumes that all constellation symbols have identical amplitudes. This assumption does not apply for many modulation schemes, such as for example Quadrature Amplitude Modulation (QAM) symbols having different amplitudes and phases. Second, since the Frequency Domain Equalizer (FDE) does not compensate polarization-mode dispersion (PMD) and polarization-dependent loss (PDL), these impairments may incorrectly bias the chromatic dispersion estimation. Third, this algorithm does not account for polarization-division multiplexing (PDM).
It should be noted that even though the MIMO equalizer 80 illustrated in FIG. 1 typically has the potential of providing very precise chromatic dispersion estimation, such post-processing estimation requires that the first CMA-based CDE delivers a reasonably small error. However, until the first CMA-based CDE delivers such a small error, a significant amount of time can lapse and frames may be lost.
In summary, a problem related to the CMA-based chromatic dispersion estimator is that the modulation format must define constellation symbols with identical amplitudes. Furthermore, the CMA-based chromatic dispersion estimator lacks robustness against polarization-mode dispersion (PMD) and polarization-dependent loss (PDL) and does not provide for polarization-division multiplexing (PDM), which can only be compensated with high implementation complexity.
The above referenced article by Kuschnerov, Maxim, et al. discloses a CMA algorithm, in which different chromatic dispersion values are tested, and the value which minimizes a defined CMA cost function is, in ideal conditions, the opposite value of the chromatic dispersion of the link. The suggested algorithm has the advantage that the estimation path uses a compensation path, wherein the signal analyzed by the estimator is the Frequency Domain Equalizer (FDE) output signal. However, the algorithm is not modulation format transparent and does not take into account PDM, PMD and PDL. US2012/0213512A1 describes a similar chromatic dispersion equalization.
Hauske, Fabian N., et al. “Frequency domain chromatic dispersion estimation.” Optical Fiber Communication Conference. Optical Society of America, 2010 discloses an estimator which works in the frequency domain and applies correlation of the input signal spectrum with a circularly-shifted version of itself. Consequently, the respective correlation power is maximized for the correct chromatic dispersion estimation. Although this estimator is transparent to the modulation format, it does not use any signal from the compensation path, leading to an increased implementation complexity. A related version of chromatic dispersion estimation is discussed in Hauske, Fabian N., et al. “Precise, robust and least complexity CD estimation.” National Fiber Optic Engineers Conference. Optical Society of America, 2011 wherein rather than analyzing the entire spectrum of the input signal, only a clock-tone is analyzed. Consequently, the implementation complexity is reduced, but the clock tone-power can be undesirably affected by polarization-related effects such as PMD and PDL. As a matter of fact, the clock tone-power can even completely vanish in certain scenarios, rendering this estimator useless for PMD impaired input signals. A similar clock-tone based approach for detecting and compensating chromatic dispersion is disclosed in US 2012/0281981A1. Here, a binary signal is modulated in pseudo-RZ modulation, which generates a clock tone in the spectrum.
The receiver monitors the power of such clock tone, which depends on the chromatic dispersion. Hence, this approach represents another clock-tone based technique having the disadvantages discussed above.
Wymeersch, Henk, and Pontus Johannisson. “Maximum-likelihood-based blind dispersion estimation for coherent optical communication.” Lightwave Technology, Journal of 30.18 (2012): 2976-2982 discloses a maximum-likelihood chromatic dispersion estimator which works in the frequency domain. This estimator is independent of the modulation format, timing offset, differential group delay (DGD) and input polarization state, and its performance is mathematically proved to be optimal. However, its implementation is very complex as it requires matrix multiplication of an oversampled input signal (more than 2 samples/symbol), and one multiplication is required per each test polarization matrix.
Sui, Qi, Alan Pak Tao Lau, and Chao Lu. “Fast and Robust Blind Chromatic Dispersion Estimation Using Auto-Correlation of Signal Power Waveform for Digital Coherent Systems.” Journal of Lightwave Technology 31.2 (2013): 306-312 discloses an estimator based on the auto-correlation of signal power waveform, but which does not search for an optimum CD value. In fact, the optimum CD value is directly the result of the estimation. However, in this scheme, the estimation path does not use any signal from the compensation path and the implementation of the estimation path is complex, as it needs a FFT/IFFT pair to calculate the correlation of the signal power waveform in the frequency domain. Furthermore, results presented in the document illustrate that the algorithm is very sensitive to narrowband electrical or optical filtering.
Hauske, Fabian N, et al. “Optical performance monitoring in digital coherent receivers.” Lightwave Technology, Journal of 27.16 (2009): 3623-3631 discloses a data-aided algorithm, which estimates the chromatic dispersion from the taps of the MIMO equalizer 80 illustrated in FIG. 1. Thus, the signals analyzed by the estimator are not the output signals of the first
Frequency Domain Equalizer (FDE) 30 in FIG. 1, but represent signals processed in a number of steps prior to being analyzed by the estimator. It follows that a useful chromatic dispersion estimation range requires very long training sequences and a very long equalizer impulse response, which can only be solved by highly complex implementations.
U.S. Pat. No. 6,798,500 relates to a method for estimation of chromatic dispersion in a multichannel optical network. Here, the disclosed estimator is based on eye-diagram analysis, wherein the chromatic dispersion distorts the eye diagram of an on-off-keying signal from its original shape. Thus, the method is limited to on-off-keying signals and can only cope with minor chromatic dispersions.
US2013/0045004 relates to a histogram-based chromatic dispersion estimator and is based on the effect that the power waveform of an optical signal subject to chromatic dispersion has a Gaussian-shaped statistical distribution. Thus, the histogram of the amplitude of the optical field is determined, and if the histogram is Gaussian, then it is concluded that the chromatic dispersion has not been properly compensated. In other words, the chromatic dispersion compensator is tuned until the histogram is no longer Gaussian. However, this estimator is applicable only to minor chromatic dispersions.
US20120128376 refers to a method of chromatic dispersion estimation for coherent receivers which is insensitive to polarization-mode dispersion (PMD). The disclosed estimator obtains two frequency parts of the signal at frequencies ±f from the center frequency. The chromatic dispersion is estimated by comparing the phase shift between the frequency parts, which should be zero if no chromatic dispersion is present in the signal. However, as polarization-related effects can additionally influence the spectral phase, this estimator is implicitly sensitive to PMD and PDL, although such influences may be reduced by averaging.
It follows that the above conventional chromatic dispersion estimators are based on time-domain signals (e.g., CMA) or frequency-domain signals (e.g., spectral analysis, clock-tone analysis) and may or may not use signals from the compensation path. However, the above conventional chromatic dispersion estimators are unsuitable or require significant complexity for coping with a modulation format with constellation symbols having unequal amplitudes, especially when the estimator is to additionally provide robustness against polarization-mode dispersion (PMD) and polarization-dependent loss (PDL) and to also account for polarization-division multiplexing (PDM).